A Perfectly Matched Layer Metric for the Electromagnetic Diffusion Field

In underwater electromagnetic communications, geophysical electromagnetic exploration, and other fields, the conduction current in the medium is much larger than the displacement current. In this case, the electromagnetic waves follow the diffusion field equation. For the simulated region truncation of the diffusion field, traditional perfectly matched layers (PMLs) for the wave equation in media that are dominated by displacement currents are not applicable. In this article, a new PML metric for the diffusion field is proposed, and its parametric form is given, which is completely different from the conventional PML formation. The parametric form is related to the frequency and conductivity of the medium and is suitable for wide frequency band and media with large conductivity ranges. The spatial distribution of characteristic parameters and the method to find the optimal characteristic parameters are introduced. The numerical experiments for 1-D, 2-D, and 3-D radiation or scattering problems verify the validity and precision of the PML through a comparison with traditional methods or analytic solutions. Through the truncation performance of different models, it is concluded that the proposed PML metric is stable and can provide a good truncation performance for the diffusion field.